Monday, February 4, 2013

You see this book. Here is philosophy. For the present I think it would still be a little beyond you - plunging into Robert Musil's Young Törless

Not enough novels are about math; that is clear enough.

The Confusions of Young Törless, Robert Musil’s 1906 debut novel, has some math.

“I say, did you really understand all that stuff?”

“What stuff?”

“All that about imaginary numbers.”

“Yes. It’s not particularly difficult, is it? All you have to do is remember that the square root of minus one is the basic unit you work with.”

“But that’s just it. I mean, there’s no such thing.” (105)

Young Törless is having an intellectual and emotional crisis, in part caused by a simple yet deep linguistic confusion. He is having difficulty relating the name of a mathematical concept to the thing-itself. Imaginary numbers are no more imaginary than real numbers are real; both are identically real and imaginary. René Descartes is endlessly smarter than either Törless or me, but this particular confusion is apparently his fault. If someone had at some point given the concept a less imaginative name – if imaginary numbers were called “Euler numbers” or “Cardano numbers” – Törless would have to go back to worrying about infinity, which he works on a bit earlier in the novel.

I remember – this is an aside – all of the confusion caused twenty or twenty-five years ago by so-called “chaos theory.” Mathematicians have proven the world is chaotic, certain hasty non-mathematicians declared, which was as wrong as could be, since the “theory” suggested that certain processes that looked random were in fact perfectly orderly and predictable. I suppose the great example of this kind of confusion is Einstein’s theory of relativity proving that all things – moral values, for example – are relative. But that is history; I lived through the chaos confusion.

If only mathematicians would restrain their poetic impulses.

Törless, who attends a boarding school, visits his math teacher’s office, hoping for enlightenment. He has apparently never been to the teacher’s office before. It is “permeated with the smell of cheap tobacco-smoke,” and the teacher’s long underwear (“rubbed black by the blacking of his boots”) is visible over his socks. Törless

could not help feeling further repelled by these little observations; he scarcely found it in him to go on hoping that this man was really in possession of significant knowledge… The ordinariness of what he saw affronted him; he projected this on to mathematics, and his respect began to give way before a mistrustful reluctance. (110)

Törless is in search of transcendent, not ordinary knowledge, beyond the scope of the teacher who urges Törless to trust math and be patient – “for the present: believe!”

But then the teacher makes a terrible error:

On a little table lay a volume of Kant, the sort of volume that lies about for the sake of appearances. This the master took up and held out to Törless.

“You see this book. Here is philosophy… For the present I think it would still be a little beyond you.” (112-3)

Which is not the right thing to say to this particular kid, although it might be good advice for me. Nevertheless, we will see how far I can get this week with Robert Musil’s little book.

Page numbers refer to the 1955 Pantheon edition, titled Young Törless. Eithne Wilkins and Ernst Kaiser were the translators.

"Imaginary numbers are no more imaginary than real numbers are real; both are identically real and imaginary."

But imaginary numbers are "imaginary" in terms of mathematics. In mathematical terms, they can't exist.

The explanation is quite simple: if you square a number, you cannot possibly get a negative result: 2 squared is 2, and -2 squared is also 2. Therefore, since the square root function is the inverse of the square function, there is no possible negative input for the square root function.

But then some mathematicians noticed that if during the course of an equation, you squared an imaginary number, then it didn't matter that the imaginary number was imaginary, because the two functions cancelled each other out.

If only they taught imaginary numbers at school these days, I'm sure more people would be interested in mathematics.

Tony - I don't know. This is the third time I have read Törless, so, yeah, read it. But it is also the only Musil I have read.

obooki, that is only true within the real number system, yes? Imaginary numbers exist within complex numbers, which exist in mathematical terms.

But the sentence you quote shows where I am cheating, how I switch from "real" as a term of mathematical jargon to "real" in its common sense meaning, as if there if anything common or sensible about it. Törless is asking the right questions! But then we see a hint of the upcoming "linguistic turn."

I don't know what y'all are doing in England, but imaginary numbers are taught in school here! Thus the hordes of engineers and mathematicians desperate for Math Fiction.

By definition ‘transcendent’ knowledge is beyond the ability of human understanding to comprehend. (It is in the realm of the ‘thing in itself’ in Kantian terms.) We have a better chance understanding the transcendental which is like studying a black hole by the effects it causes on the edges where we can grasp a glimpse.

Some math descriptions require poetry in the same way that some mystical experiences can only be described by poetry. It is interesting that the poetry seems to be the same throughout time and independent of cultures. I particularly like the term ‘charm’ as used in subatomic physics.

When you try to understand the un-understandable, don’t expect to be understood.

I know a guy who works with field equations and electromagnetic radiation (if I understand him correctly, which I'm pretty sure I really don't) and he does a lot of math. He's said more than once that at a certain point, language breaks down and is no longer able to communicate what he's doing with his mathematics; the two systems pull away from each other with increasing rapidity. "I end up, more or less, speaking in philosophical haiku when I have to discuss my work with people outside my field," he says. I paraphrase. Anyway, we need more art about mathematics. Plays, poems, paintings and novels. Musil sounds like a hoot.

I was introduced to imaginary numbers in school but we did not get along and so are no longer on speaking terms. We studiously ignore each other when, on those rare occurences, we are invited to the same parties.

I regularly have to read research statements from academics in mathematics, a field about which I know almost nothing. I truly wish some of them would - could - describe their no doubt fascinating work in "philosophical haiku."

Of course, in another sense his language is perfectly adequate - for communicating with other people who share the language.

Törless does not have a technical language, which reinforces of perhaps even causes his crisis: "Nevertheless, he was dreadfully agitated, and the fear of not being able to make himself intelligible almost exhausted him" (205).

I suppose I should write something about what the book is about in the usual sense. Not imaginary numbers.

Aside from Flatland, I don't know if I can name any off the top of my head.

There's an intriguing line in Vassily Grossman's Life and Fate in which the scientist Viktor Shtrum's wife suggests that he write the War and Peace of physics, which, for the scientific community, would be an interesting companion volume to have alongside the War and Peace of Grossman.

Playful, huh? Just pokes fun, you don't say? Now I know what to cover in tonight's post. Up to a point, Lord Copper.

This really is an intensely teenage novel (or, obviously, an adult's representation of teenage confusions). I have come across readers who dislike Catcher in the Rye simply because it is about an intense teenager. Those people should avoid this book.

Borges recommends Charles Hinton's Scientific Romances (1884) which are partly about math. Flatland is a little marvel. I am not sure that I really do want more fiction about math. There might already be exactly the ideal amount.

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I too could now say to myself: Be no longer a Chaos, but a World, or even Worldkin. Produce! Produce! Were it but the pitifullest infinitesimal fraction of a Product, produce it in God's name! 'Tis the utmost thou hast in thee; out with it then. Up, up! Whatsoever thy hand findeth to do, do it with thy whole might. Work while it is called To-day, for the Night cometh wherein no man can work.